In magnetic disk drive storage devices, sampled amplitude read channels employing partial response (PR) signaling with maximum likelihood (ML) sequence detection have provided a substantial increase in storage capacity by enabling significantly higher linear bit densities. Partial response signaling refers to a particular method for transmitting symbols represented as analog pulses through a communication medium. The benefit is that at the signaling instances (baud rate) there is no intersymbol interference (ISI) from other pulses except for a controlled amount from immediately adjacent, overlapping pulses. Allowing the pulses to overlap in a controlled manner leads to an increase in the symbol rate (linear recording density) without sacrificing performance in terms of signal-to-noise ratio (SNR).
Partial response channels are characterized by the polynomials(1−D)(1+D)n where D represents a delay of one symbol period and n is an integer. For n=1,2,3, the partial response channels are referred to as PR4, EPR4 and EEPR4, with their respective frequency responses shown in FIG. 1A. The channel's dipulse response, the response to an isolated symbol, characterizes the transfer function of the system (the output for a given input). With a binary “1” bit modulating a positive dipulse response and a binary “0” bit modulating a negative dipulse response, the output of the channel is a linear combination of time shifted dipulse responses. The dipulse response for a PR4 channel (1−D2) is shown as a solid line in FIG. 1B. Notice that at the symbol instances (baud rate), the dipulse response is zero except at times t=0 and t=2. Thus, the linear combination of time shifted PR4 dipulse responses will result in zero ISI at the symbol instances except where immediately adjacent pulses overlap.
It should be apparent that the linear combination of time shifted PR4 dipulse responses will result in a channel output of +2, 0, or −2 at the symbol instances (with the dipulse samples normalized to +1, 0, −1) depending on the binary input sequence. The output of the channel can therefore be characterized as a state machine driven by the binary input sequence, and conversely, the input sequence can be estimated or demodulated by running the signal samples at the output of the channel through an “inverse” state machine. Because noise will obfuscate the signal samples, the inverse state machine is actually implemented as a trellis sequence detector which computes a most likely input sequence associated with the signal samples.
The performance of the trellis sequence detector in terms of bit error rate depends on the amount of noise in the system, including noise due to the spectrum of the read signal diverging from the ideal partial response. Linear distortions in the read signal can generally be suppressed using a linear equalizer which may operate on the continous-time analog read signal or the discrete-time samples of the read signal. Typical read channels employ both an analog equalizer, such as a biquad analog filter, followed by a nth order finite-impulse response (FIR) discrete-time filter. Linear equalizers, however, are not effective in attenuating non-linear distortions in the read signal, such as asymmetries caused by the non-linear response of a magneto-resistive (MR) read head.
An MR read head comprises an MR sensor element with a resistance which is proportional to the strength of the magnetic flux; the read signal is generated by applying a current to the MR element and measuring the voltage across it as it passes over the magnetic transitions recorded on the disk. FIG. 2A is a plot of the head's resistance versus the magnetic flux which illustrates that the response can be very non-linear. The asymmetry effect of this non-linearity on the read signal is illustrated in FIG. 2B which shows the head's response to an isolated positive and negative magnetic transition. In this example, the magnitude of the pulse induced by the positive magnetic transition is greater than the magnitude of the pulse induced by the negative magnetic transition (note that the asymmetry in the pulses may be reversed, and other asymmetries may also be present in the read signal). Ultimately, the non-linear distortions prevent the read signal from attaining the desired partial response target, introducing noise into the sample values which degrades the performance of the trellis sequence detector. This undesirable effect is generally ameliorated by applying a magnetic biasing field across the MR element so that it operates in a linear region of the response while still providing sufficient sensitivity and stability. However, biasing the MR element does not remove the non-linear aberrations from the read signal entirely, particularly when errors in the biasing field move the MR element away from the optimal linear region of operation.
There is, therefore, a need for an improved sampled amplitude read channel for use in disk storage systems that provides a non-linear correction circuit for correcting non-linear distortions in the read signal, such as asymmetries caused by the non-linear response of an MR read head.